Direct Cartesian-Space Solutions of Generalized Bloch Equations in the Rotating Frame

Analytical solutions of the generalized Bloch equations for an arbitrary set of initial values of the x, y, and z magnetization components are given in the rotating frame. The solutions involve the decoupling of the three coupled differential equations such that a third-order differential equation in each magnetization variable is obtained. In contrast to the previously reported solutions given by Torrey, the present attempt paves the way for more direct physical insight into the behavior of each magnetization component. Special cases have been discussed that highlight the utility of the general solutions. Representative trajectories of magnetization components are given, illustrating their behavior with respect to the values of off-resonance and initial conditions. (C) 1995 Academic Press, Inc.

Nematogens with more flexible chains than aromatic rings in the core

Mesogens containing four rings in the main core can accommodate one terminal and two nearby lateral chains on each outside aromatic ring. These compounds containing six chains present an enantiotropic nematic range which is influenced by the rigidity of the links. The conformational behaviour of the first methyleneoxy group within the chains was investigated by one and two dimensional C-13 NMR. The sign of the jump in chemical shifts when entering the nematic phase indicates the folding of each lateral branch. Dipolar oscillations during cross-polarization contact provide the values of the bond order parameter. The two First lateral fragments do not behave in the same way, demonstrating the influence of the fragment along which the chain is back: folded.

Stability of non-parabolic flow in a flexible tube

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such 'non-parabolic' flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Solid state structural and solution studies on the formation of a flexible cavity for anions by copper(I) and 1,2-bis(diphenylphosphino)ethane

Copper(l) complexes of 1,2-bis(diphenylphosphino)ethane (dppe) with a stoichiometry Cu-2(dppe)(3)(X)(2) [X- = CN- (1), SCN- (2), NO3- (3)] are obtained from direct reactions of CuX and dppe. The complexes are structurally and spectroscopically (NMR and IR) characterized. The structure of the [Cu-2(dPPe)(3)](2+) dication is similar to the structural motif observed in many other complexes with a chelating dppe and a bridging dppe connecting two copper centers. In complexes 1 -3, the anions are confined to the cavity formed by the phosphines which force a monodentate coordination mode despite the predominant bidentate/bridging character of the anions. The coordination angles rather than the thermochemical radii dictate the steric requirement of anions. While the solution behavior of 3, with nitrate, is similar to complexes studied earlier, complexes with pseudohalides exhibit new solution behavior. (C) 2002 Elsevier Science Ltd. All rights reserved.

A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17–550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor $f$ is measured as a function of the Reynolds number $Re$. From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the $f$–$Re$ curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of $16\ensuremath{/} Re$ in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

A Compliant Mechanism Kit with Flexible Beams and Connectors

We present the concept, prototypes, and an optimal design method for a compliant mechanism kit as a parallel to the kits available for rigid-body mechanisms. The kit consists of flexible beams and connectors that can be easily hand-assembled using snap fits. It enables users, using their creativity and mechanics intuition, to quickly realize a compliant mechanism. The mechanisms assembled in this manner accurately capture the essential behavior of the topology, shape, size and material aspects and thereby can lead the way for a real compliant mechanism for practical use. Also described in this paper are the design of the connector to which flexible beams can be added in eight different directions; and prototyping of the spring steel connectors as well as beams using wire-cut electro discharge machining. It is noted in this paper that the concept of the kit also resolves a discrepancy in the finite element (FE) modeling of beam-based compliant mechanisms. The discrepancy arises when two or more beams are joining at one point and thus leading to increased stiffness. After resolving this discrepancy, this work extends the topology optimization to automatically generate designs that can be assembled with the kit. Thus, the kit and the accompanying analysis and optimal synthesis procedures comprise a self-contained educational as well as a research and pragmatic toolset for compliant mechanisms. The paper also illustrates how human creativity finds new ways of using the kit beyond the original intended use and how it is useful even for a novice to design compliant mechanisms.

Design and Implementation of a Flexible and Memory Efficient Operating System for Sensor Nodes

Sensor network nodes exhibit characteristics of both embedded systems and general-purpose systems.A sensor network operating system is a kind of embedded operating system, but unlike a typical embedded operating system, sensor network operatin g system may not be real time, and is constrained by memory and energy constraints. Most sensor network operating systems are based on event-driven approach. Event-driven approach is efficient in terms of time and space.Also this approach does not require a separate stack for each execution context. But using this model, it is difficult to implement long running tasks, like cryptographic operations. A thread based computation requires a separate stack for each execution context, and is less efficient in terms of time and space. In this paper, we propose a thread based execution model that uses only a fixed number of stacks. In this execution model, the number of stacks at each priority level are fixed. It minimizes the stack requirement for multi-threading environment and at the same time provides ease of programming. We give an implementation of this model in Contiki OS by separating thread implementation from protothread implementation completely. We have tested our OS by implementing a clock synchronization protocol using it.

Speech Enhancement using Intra-frame Dependency in DCT Domain

In this paper, we present a new speech enhancement approach, that is based on exploiting the intra-frame dependency of discrete cosine transform (DCT) domain coefficients. It can be noted that the existing enhancement techniques treat the transformdomain coefficients independently. Instead of this traditional approach of independently processing the scalars, we split the DCT domain noisy speech vector into sub-vectors and each sub-vector is enhanced independently. Through this sub-vector based approach, the higher dimensional enhancement advantage, viz. non-linear dependency, is exploited. In the developed method, each clean speech sub-vector is modeled using a Gaussian mixture (GM) density. We show that the proposed Gaussian mixture model (GMM) based DCT domain method, using sub-vector processing approach, provides better performance than the conventional approach of enhancing the transform domain scalar components independently. Performance improvement over the recently proposed GMM based time domain approach is also shown.

Realizing a flexible constraint length Viterbi decoder for software radio on a de Bruijn interconnection network

Building flexible constraint length Viterbi decoders requires us to be able to realize de Bruijn networks of various sizes on the physically provided interconnection network. This paper considers the case when the physical network is itself a de Bruijn network and presents a scalable technique for realizing any n-node de Bruijn network on an N-node de Bruijn network, where n < N. The technique ensures that the length of the longest path realized on the network is minimized and that each physical connection is utilized to send only one data item, both of which are desirable in order to reduce the hardware complexity of the network and to obtain the best possible performance.

Generalized asymptotic expansions for the wavenumbers in infinite flexible in vacuo orthotropic cylindrical shells

Analytical expressions are found for the wavenumbers and resonance frequencies in flexible, orthotropic shells using the asymptotic methods. These expressions are valid for arbitrary circumferential orders n. The Donnell-Mushtari shell theory is used to model the dynamics of the cylindrical shell. Initially, an in vacuo cylindrical isotropic shell is considered and expressions for all the wavenumbers (bending, near-field bending, longitudinal and torsional) are found. Subsequently, defining a suitable orthotropy parameter epsilon, the problem of wave propagation in an orthotropic shell is posed as a perturbation on the corresponding problem for an isotropic shell. Asymptotic expressions for the wavenumbers in the in vacuo orthotropic shell are then obtained by treating epsilon as an expansion parameter. In both cases (isotropy and orthotropy), a frequency-scaling parameter (eta) and Poisson's ratio (nu) are used to find elegant expansions in the different frequency regimes. The asymptotic expansions are compared with numerical solutions in each of the cases and the match is found to be good. The main contribution of this work lies in the extension of the existing literature by developing closed-form expressions for wavenumbers with arbitrary circumferential orders n in the case of both, isotropic and orthotropic shells. Finally, we present natural frequency expressions in finite shells (isotropic and orthotropic) for the axisymmetric mode and compare them with numerical and ANSYS results. Here also, the comparison is found to be good. (C) 2011 Elsevier Ltd. All rights reserved.

TeV scale implications of non commutative space time in laboratory frame with polarized beams

We analyze e(+)e(-) -> gamma gamma, e(-)gamma -> e(-)gamma and gamma gamma -> e(+)e(-) processes within the Seiberg-Witten expanded noncommutative scenario using polarized beams. With unpolarized beams the leading order effects of non commutativity starts from second order in non commutative(NC) parameter i.e. O(Theta(2)), while with polarized beams these corrections appear at first order (O(Theta')) in cross section. The corrections in Compton case can probe the magnetic component(Theta(B)) while in Pair production and Pair annihilation probe the electric component((Theta) over right arrow (E)) of NC parameter. We include the effects of earth rotation in our analysis. This study is done by investigating the effects of non commutativity on different time averaged cross section observables. The results which also depends on the position of the collider, can provide clear and distinct signatures of the model testable at the International Linear Collider(ILC).